论文标题
Dirichlet形式的潜在理论，跳跃内核在边界处爆炸
Potential theory of Dirichlet forms with jump kernels blowing up at the boundary
论文作者
论文摘要
在本文中，我们研究了一半空间$ \ mathbb {r}^d _+$在跳跃内核$ j（x，x，y）= | x-y |^{ - d-d-α} \ mathcal {b}（x，x，y）$和杀死潜在的$κX_d^^{$ at的$α}的$ j（x，b}（$ $ \ MATHCAL {B}（X，Y）$可以在边界处爆炸到Infinity。跳跃内核和杀戮潜力取决于几个参数。对于所涉及的参数和所有$ d \ ge 1 $的所有可接受的值，我们证明了边界harnack原理，并在这些过程的绿色函数上建立尖锐的双向估计。
In this paper we study the potential theory of Dirichlet forms on the half-space $\mathbb{R}^d_+$ defined by the jump kernel $J(x,y)=|x-y|^{-d-α}\mathcal{B}(x,y)$ and the killing potential $κx_d^{-α}$, where $α\in (0, 2)$ and $\mathcal{B}(x,y)$ can blow up to infinity at the boundary. The jump kernel and the killing potential depend on several parameters. For all admissible values of the parameters involved and all $d \ge 1$, we prove that the boundary Harnack principle holds, and establish sharp two-sided estimates on the Green functions of these processes.
